1. Field of the Invention
The present invention relates to an optical apparatus capable of simultaneously obtaining a plurality of Fourier transform patterns of a transmission object under illumination of coherent light.
2. Description of the Prior Art
In the field of optical information processing or so-called "optical computing", there is an approach to a high-speed matrix operation, an interimage operation and the like utilizing a parallelistic property of light. For example, there is an approach to simultaneously obtaining a plurality of Fourier transform patterns of an image (transmission object) which is formed into information by a transmittivity or a phase and causing each pattern to perform a predetermined image operation.
For this purpose, an optical apparatus capable of simultaneously obtaining a plurality of Fourier transform patterns of a transmission object with a simple arrangement is necessary.
A known conventional apparatus of this type is shown in FIG. 1 or 2.
Referring to FIG. 1, coherent light emitted from an HeNe laser 1 is spatially expanded into a collimated light beam by a beam expander 2 and illuminates a transmission object 3. Two-dimensional matrix pin hole array 4 is located immediately after the transmission object 3, and a lens 5 is arranged thereafter. The transmission object 3 is arranged near a front focal surface of the lens 5. With this arrangement, a plurality of Fourier transform patterns of the transmission object 3 are obtained on a rear focal surface 6 of the lens 5.
Assuming that a complex transmittivity of the transmission object 3 is f(x,y) and a pin hole diameter of the pin hole array 4 is sufficiently small, f(x,y) sampled by the pin hole array 4 is represented as follows by using a Dirac function: ##EQU1## (1) where each of p and q is the pitch of a pin hole.
Therefore, a Fourier transform pattern of relation (1) obtained by the lens 5 is given as follows assuming that F(.xi.,n) is a Fourier transform of f(x,y): ##EQU2## (2) That is, a plurality of Fourier transform patterns F(.xi.,.eta.) of f(x,y) are obtained on the (.xi.,.eta.) plane, i.e., the rear focal surface of the lens 5.
In the above relation, symbol * represents convolution. Each of 1/p' and 1/q' represents the pitch between patterns F(.xi.,.eta.) on the Fourier transform surface. In this case, p and q are proportional to p'and q', respectively. Therefore, the pitch between the pin hole array is inversely proportional to the pitch between the Fourier transform patterns.
FIG. 2 shows another conventional technique capable of obtaining a plurality of Fourier transform patterns by using a computer hologram.
A collimated coherent light beam obtained by an arrangement similar to that shown in FIG. 1 illuminates the transmission object 3. A computer hologram 7 is arranged after the transmission object 3.
The computer hologram 7 is so coded as to reproduce matrix point array at a position separated from a hologram surface by a predetermined interval when collimated coherent illumination is used as reference light. More specifically, as shown in FIG. 3, a pattern in which a plurality of so-called Fresnel zone plates overlap to be offset from each other is recorded. In FIG. 3, only two patterns are shown for illustrative simplicity.
With the above arrangement, a Fourier transform pattern of the transmission object 3 can be obtained about each point reproduced by the computer hologram.
The apparatus shown in FIG. 1, however, is problematic because an amount of light transmitted through the pin hole to sample the object is significantly small and therefore the obtained Fourier transform pattern is very dark.
When a pin hole diameter is increased to solve this problem, Fourier transform H(.xi.,.eta.) of a complex transmittivity h (x,y) of the pin hole is added to the Fourier transform pattern. As a result, relation 2 is rewritten as follows: ##EQU3## That is, when the pin hole h(x,y) is enlarged, the cutoff frequency of the Fourier transform H(.xi.,.eta.) moves to a low-frequency side. Therefore, the obtained Fourier pattern lacks high-frequency information.
With the arrangement shown in FIG. 2, the computer hologram in which a plurality of Fresnel zone plates overlap each other is used to obtain a plurality of Fourier transform patterns. In this case, in addition to the +lst diffracted light component required to obtain the Fourier transform patterns, unnecessary diffracted light components such as 0th, -lst and +2nd diffracted light components are generated. In addition, diffracted light is generated due to mutual interference (so-called moire) between the zone plates. As a result, noise patterns of these unnecessary diffracted light components significantly overlap the Fourier transform patterns.